Taarabt, 21, has signed a three-year contract with the Hoops, who are paying a fee of around £1million. He scored seven goals on loan at the club last season.
"I'm glad to have finally tied Adel up, he's a player who has got a unique talent," said the R's manager Neil Warnock.
"We're delighted to have him on board and he gives us that little bit of quality that you need. I think it's good for him that he knows where he's going to be permanently now. Long term, his target is still to play at the very top level, and I'm hoping that we can help him to achieve that."
Hull City have had Tottenham Hotpsur midfielder John Bostock training with them this week, but are unable to complete the signing on a loan deal unless they sell players or receive part of the parachute payment the Premier League have threatened to withhold.
The Premier League should give the Tigers £9million as part of their controversial payments to clubs relegated to the Championship, but threatened to instead give this money to their clubs owed money in transfer fees by the Tigers.
Hull are in talks with the Premier League, with BBC Radio Humberside saying they expect an agreement where the East Yorkshire side receive part of the payment so long as they agree terms with clubs owed money.
"We can't do any business until the financial situation is resolved, which we are confident will happen," manager Nigel Pearson said.
Middlesbrough have turned down a £2million bid from the Premier League side Liverpool for goalkeeper Brad Jones.
Marton Fulop has completed a move from Sunderland to Ipswich Town. The goalkeeper, 27, has moved for an undisclosed fee and is reunited with manager Roy Keane, who he worked with at the Black Cats.
On his way out of Portman Road is midfielder Owen Garvan, who has moved to Crystal Palace for an undisclosed fee.
Roberto Martinez hopes Wales international Jason Koumas can kick-start his career after allowing the midfielder to join Cardiff City on a season-long loan.
The Bluebirds must wait until a Football League transfer embargo is lifted before the deal can be concluded.
"It's not done yet, because obviously there is an embargo situation with Cardiff City," Martinez told the Evening Post.
"So, until the FA tell us otherwise, we can't really confirm anything. But we all hope the deal goes through and he does very well for his new club.
"It depends very much on the Cardiff end, but I would imagine it will get sorted pretty quickly."
Nottingham Forest have signed the England U21 left-back Ryan Bertrand on loan from the Premier League side Chelsea until January.
Bertrand has plenty of Football League experience, having already been out on loan to Norwich City, Bournemouth and Oldham Athletic.
Bristol City have signed striker Sam Vokes on loan from Wolves until January.
Preston North End have signed of versatile midfielder Darel Russell, 29, on a Bosman transfer from Norwich City.